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The 6563 Å H_{α} line emitted by hydrogen in a star is found to be redshifted by 15 Å. Estimate the speed with which the star is receding from the Earth.

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#### Solution

Wavelength of `"H"_alpha` line emitted by hydrogen,

λ = 6563 Å

= 6563 × 10^{−10} m

Star’s red-shift, (λ' − λ) 15 Å = 15 × 10^{−10} m

Speed of light, c = 3 × 10^{8} m/s

Let the velocity of the star receding away from the Earth be v.

The red shift is related with velocity as:

`lambda"'" - lambda = "v"/"c" lambda`

`"v" = "c"/lambda xx (lambda"'" - lambda)`

= `(3 xx 10^8 xx 15 xx 10^(-10))/(6563 xx 10^(-10))`

= 6.87 × 10^{5} m/s

Therefore, the speed with which the star is receding away from the Earth is 6.87 × 10^{5}m/s.

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